Title A Hierarchical Canonical Labelling and its Application in Generation of Graphs Seyedeh Narjess Afzaly (Australian National University) Seyedeh Narjess Afzaly Algebra and Discrete Mathematics 15:00:00 2017-09-25 We present a new class of canonical labellings, \textit{hierarchical canonical labelling}, for graphs in which if the vertices of a graph $G$ are canonically labelled by $\{1, \dots, n\}$, then $G\setminus\{n\}$ is also canonically labelled. We provide examples of such canonical labellings. As an application of these labellings, we introduce a new method of generation based on this labelling that combines the benefits of two well-known methods of generation: Orderly Generation and Generation by Canonical Construction Path.